http://arxiv.org/pdf/1111.4503v1.pdf
There's 125 billion friendships and 900 million monthly active.
125 billion / 900 million = 139 friendship pairs / user
A pair = 2 friends so you double it to get 278 friends/users.
This is of course an overestimate as people are friends with people who use fb < once a month. Not sure what total user count is though.